IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Number-Upper and Lower Bounds
Topic :Number- Weightage : 21 %
All Questions for Topic : Laws of exponents, including fractional/rational exponents Logarithms, including laws of logarithms and the use of technology to find values Upper and lower bounds
Question
Izumi is a volunteer at a pet rescue centre which has cats, dogs and rabbits for adoption. At the next school festival, she will try to convince students to adopt a pet from the pet rescue centre.
Izumi decides to run a survey in her school before the festival.
She asked the following questions:
The image and Venn diagram show the survey results for the girls.
Event $\mathrm{C}$ represents: Would like to adopt a cat
Event $\mathrm{D}$ represents: Would like to adopt a dog
Event $\mathrm{R}$ represents: Would like to adopt a rabbit
No girl selected more than one pet.
Question (a)
Determine the percentage of girls who would not like to adopt a pet. Write your answer on the Venn diagram.
▶️Answer/Explanation
Ans:
\( \begin{aligned} & =[100-(41+29+26)] \% \\ & =4 \%\end{aligned} \)
Question (b)
Events $\mathrm{C}, \mathrm{D}$ and $\mathrm{R}$ are mutually exclusive. State how this is represented in the Venn diagram.
▶️Answer/Explanation
Ans:
$A \cap B \cap C=0$ or $\varnothing$
In the context of your scenario with the Venn diagram representing the survey results for the girls, the mutually exclusive nature of events $\mathrm{C}$ (Would like to adopt a cat), $\mathrm{D}$ (Would like to adopt a dog), and $\mathrm{R}$ (Would like to adopt a rabbit) means that no girl selected more than one pet. Each girl’s response falls into one and only one of these categories.
So, in the Venn diagram, you would have three separate circles representing events $\mathrm{C}$, $\mathrm{D}$, and $\mathrm{R}$ with no overlapping regions between them. This visually demonstrates that the events are mutually exclusive, and each girl’s preference falls into one specific category.